Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 41 x + 695 x^{2} - 5699 x^{3} + 19321 x^{4}$ |
Frobenius angles: | $\pm0.105232638034$, $\pm0.208549921524$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.2043717.2 |
Galois group: | $D_{4}$ |
Jacobians: | $16$ |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
$p$-rank: | $1$ |
Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14277$ | $367732689$ | $7211121088383$ | $139362633210982077$ | $2692477571943557577072$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $99$ | $19031$ | $2685087$ | $373325059$ | $51889333584$ | $7212555350435$ | $1002544419254169$ | $139353667491212755$ | $19370159742952286361$ | $2692452204199262558486$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=35x^6+90x^5+130x^4+77x^3+85x^2+54x+19$
- $y^2=133x^6+126x^5+73x^4+53x^3+96x^2+65x+48$
- $y^2=136x^6+77x^5+75x^4+61x^3+129x^2+129x+128$
- $y^2=89x^6+21x^5+98x^4+84x^3+25x^2+78x+45$
- $y^2=6x^6+64x^5+31x^4+9x^3+73x^2+127x+24$
- $y^2=40x^6+47x^5+72x^4+21x^3+17x^2+31x+133$
- $y^2=85x^6+104x^5+134x^4+74x^3+71x^2+95x+90$
- $y^2=46x^6+98x^5+97x^4+39x^3+32x+57$
- $y^2=115x^6+111x^5+130x^4+90x^3+45x^2+89x+23$
- $y^2=87x^6+102x^5+123x^4+137x^3+110x^2+124x+138$
- $y^2=69x^6+119x^5+11x^4+73x^3+27x^2+130x+103$
- $y^2=68x^6+4x^5+25x^4+52x^3+92x^2+65x+122$
- $y^2=21x^6+136x^5+19x^4+74x^3+89x^2+23x+57$
- $y^2=6x^6+90x^5+13x^4+85x^3+41x^2+95x+85$
- $y^2=41x^6+54x^5+67x^4+34x^3+110x^2+88x+40$
- $y^2=33x^6+12x^5+8x^4+39x^3+126x^2+97x+107$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{139}$.
Endomorphism algebra over $\F_{139}$The endomorphism algebra of this simple isogeny class is 4.0.2043717.2. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
2.139.bp_bat | $2$ | (not in LMFDB) |